Question: Determine the intercepts of the line. $ y=-7x+3$ $y$ -intercept: $\Big($
Solution: The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}y&=-7\cdot{0}+3\\ y&=3\end{aligned}$ So the $y$ -intercept is $\left(0,3\right)$. Generally, in linear equations of the form $y=m\!\!\,\cdot\!\!x+b$ (which is called slope-intercept form ), the $y$ -intercept is $(0,b)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}{0}&=-7x+3\\ 7x&=3\\ x&=\dfrac{3}{7}\end{aligned}$ So the $x$ -intercept is $\left(\dfrac{3}{7},0\right)$. In conclusion, The $y$ -intercept is $\left(0,3\right)$. The $x$ -intercept is $\left(\dfrac{3}{7},0\right)$.